Such an infinitely variable transmission is e.g. known from the German Offenlegungsschrift No. 2118083. The limitation of the filling hole used there is that, in order to be able to ensure that there is constantly sufficient pressure in the cylinder space, the filling hole cannot be too large because otherwise, especially at higher pressures, too much fluid will flow away via the filling hole in the compensation chamber. The drawback of too small a hole on the other hand is that the filling hole becomes clogged easily, so that the action of the compensation chamber is limited or lost entirely. This drawback has largely been obviated in a steplessly variable transmission according to the Dutch patent application No. 8302089, the disclosure of which is also available in U.S. Pat. No. 4,575,364 to Lamers. This known infinitely variable transmission is also provided with a filling hole as described above but before this filling hole, at the side of the cylinder space, a filter is provided. This filter has a number of passages which together form a considerably larger passage diameter than that of the filling hole, the diameter of each passage being smaller than that of the filling hole, however. The infinitely variable transmission with a filling hole provided with a filter functions well by itself, but its drawback is that after a long time rather a great deal of impurities is collected in the cylinder space and before the filter, which impurities restrict the proper functioning in the long run. Moreover, such a filter is relatively expensive. The purpose of the invention is to obviate the above drawbacks of the known infinitely variable transmission.